If $p$ is a prime where $p \equiv 3 \pmod{4}$ then $p$ can't be written as the sum of two numbers squared.

I attempted by contradiction, supposing that $p=a^2 + b^2$ where $a,b$ are integers. From definitions i got down to $4$ must divide $a^2 + b^2 - 3$ (since $p=a^2 + b^2\equiv 3 \pmod{4} )$ but I am unsure why this is (or leads to) a contradiction.